Polyulya D. Weak solutions of the stochastic partial differential equations driven by general stochastic measures

Ph.D. thesis is devoted to the study of stochastic wave equation and heat equation driven by general stochastic measures. The random influence in the equations is given by stochastic integrals of real-valued functions. The existence and uniqueness of the weak solution of Cauchy problem were considered. For the wave equation and unknown process, in the case of two and three spatial variables, the existence of the solution was proved and explicit solutions were given. For the wave equation and heat equation, sufficient conditions of the uniqueness of the solutions in special class of processes are obtained. The class of processes is described in terms of integrals with respect to general stochastic measures. The stochastic wave equation and stochastic heat equation with respect to unknown generalized random function are considered. Sufficient conditions for the existence and uniqueness of the solutions of the Cauchy problem were obtained.